My Time at Portia is a great game, but it can be a bit tricky to understand exactly how you save the game. There is no save points or even quick save features, and instead you have to save by going to bed. Every time you go to sleep, the game saves, and you can exit if you feel like it.
It is currently impossible to save mid-day, and you must head to your bed to save. However, it's possible to go to bed at any time, so you can save your progress even if it's early in the morning by going to bed when you want to.